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C.1 Simple harmonic motion - IB Questionbank | RevisionDojo

Practice C.1 Simple harmonic motion with authentic IB Physics exam questions for both SL and HL students. This question bank mirrors Paper 1A, 1B, 2 structure, covering key topics like mechanics, thermodynamics, and waves. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SLPaper 2

The graph shows the displacement-time representation of two transverse waves (solid and dashed) travelling through the same medium. Both waves have the same amplitude and frequency.

State the amplitude of either wave.

[1]

Determine the period of the waves.

[2]

Determine the phase difference between the two waves.

[2]

Outline one difference between the two waves other than phase.

[1]

Explain how the graph supports the principle of superposition.

[2]

Question 2

SLPaper 2

The graph shows the transverse displacement $s$ in millimetres of points on a stretched string as a function of distance $d$ in metres along the string at a fixed instant in time.

State the amplitude of the wave.

[1]

State the wavelength of the wave.

[1]

The wave has a frequency of $5.0\ \mathrm{Hz}$ . Calculate the speed of the wave.

[2]

Identify whether this is a transverse or longitudinal wave. Justify your answer.

[2]

Question 3

SLPaper 2

A student investigates a mass-spring system undergoing vertical simple harmonic motion. The system has a spring constant $k = 50.0\ \text{N m}^{-1}$ and supports a mass of $0.40\ \text{kg}$ . The system oscillates with an amplitude of $0.10\ \text{m}$ .

Calculate the natural frequency of the oscillation.

[2]

Calculate the total mechanical energy of the system.

[2]

Determine the displacement of the mass when the speed is $0.50\ \text{m s}^{-1}$ .

[2]

Explain how damping would affect the amplitude and energy of this system over time.

[2]

Question 4

HLPaper 1A

A body moves in simple harmonic motion (SHM). At time $t = 0$ , the displacement is zero and the body is moving in the positive direction.

Which graph correctly shows the variation of the body's kinetic energy $E_k$ with time?

Question 5

SLPaper 2

The graph shows the displacement $s$ in millimetres of a point on a string as a function of time $t$ in seconds.

State the type of wave represented by the graph.

[1]

Determine the amplitude and period of the wave.

[2]

Calculate the frequency of the wave.

[2]

Outline how you could confirm whether this motion represents simple harmonic motion.

[2]

Sketch a graph of the velocity of the point against time, from $t = 0$ to $t = 0.40\ \mathrm{s}$ .

[3]

Question 6

SLPaper 1A

What is the phase difference between velocity and acceleration in simple harmonic motion?

Question 7

SLPaper 2

A $0.50\ \text{kg}$ mass is attached to a spring and performs simple harmonic motion with an amplitude of $0.10\ \text{m}$ and a maximum speed of $1.20\ \text{m s}^{-1}$ .

State the relationship between maximum speed, amplitude, and angular frequency.

[1]

Calculate the angular frequency of the motion.

[2]

Determine the period of the oscillation.

[2]

Question 8

HLPaper 2

A particle moves according to the equation $x(t) = 0.20 \cos(8t - \frac{\pi}{6})$ (in metres and seconds).

Determine the displacement and velocity of the particle at $t = 0.25\ \text{s}$ .

[3]

Calculate the maximum speed of the particle.

[1]

Determine the total energy of the system if the mass of the particle is $0.10\ \text{kg}$ .

[2]

Calculate the potential energy of the particle at $t = 0.25\ \text{s}$ .

[2]

Explain the meaning of negative velocity in this context.

[1]

Question 9

HLPaper 1B

A student investigates the damping of a pendulum's amplitude $(A)$ over time $(t)$ . The amplitude is measured at regular time intervals as the pendulum oscillates in air. The following data were recorded:

Time $(t)(\mathbf{s})$	Amplitude $(A)(\mathrm{cm})$
0	10.0
5	8.1
10	6.6
15	5.4
20	4.4
25	3.6
30	3.0

The amplitude of a damped oscillation follows the equation:

A(t)=A_0 e^{-\frac{b}{m} t}

where:

$A_0$ is the initial amplitude $(t=0)$ ,
$b$ is the damping coefficient,
$m$ is the mass of the pendulum bob,
$t$ is the time,
$e$ is the base of the natural logarithm.

Describe the trend in the graph and explain how it relates to the equation $A(t)=$ $A_0 e^{-\frac{b}{m} t}$ .

[2]

Identify two potential sources of error in the experiment and explain their impact on the measured amplitude.

[4]

Suggest two improvements to minimize these errors.

[2]

Suggest how to linearize the data to determine the damping coefficient $\frac{b}{m}$ .

[2]

Using the data point $A=6.6 \mathrm{~cm}, t=10 \mathrm{~s}, A_0=10.0 \mathrm{~cm}$ , calculate the value of $\frac{b}{m}$ . Show all your working.

[3]

If the uncertainty in $A$ is $\pm 0.1 \mathrm{~cm}$ and the uncertainty in $t$ is $\pm 0.5 \mathrm{~s}$ , calculate the percentage uncertainty in $\frac{b}{m}$ for the same data point.

[3]

Question 10

HLPaper 1A

A particle undergoes simple harmonic motion. Which quantities of the motion can be simultaneously zero?

C.1 Simple harmonic motion Questionbank